Question: Simplify the following expression: $ y = \dfrac{-5}{4} + \dfrac{-2}{-7x - 6} $
Answer: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{-7x - 6}{-7x - 6}$ $ \dfrac{-5}{4} \times \dfrac{-7x - 6}{-7x - 6} = \dfrac{35x + 30}{-28x - 24} $ Multiply the second expression by $\dfrac{4}{4}$ $ \dfrac{-2}{-7x - 6} \times \dfrac{4}{4} = \dfrac{-8}{-28x - 24} $ Therefore $ y = \dfrac{35x + 30}{-28x - 24} + \dfrac{-8}{-28x - 24} $ Now the expressions have the same denominator we can simply add the numerators: $y = \dfrac{35x + 30 - 8}{-28x - 24} $ $y = \dfrac{35x + 22}{-28x - 24}$ Simplify the expression by dividing the numerator and denominator by -1: $y = \dfrac{-35x - 22}{28x + 24}$